Chapter 1: Whole Numbers

Transcription

1 Chapter 1: Whole Numbers Prep Test a and D; b and E; c and A; d and B; e and F; f and C.. Fifty Go Figure On the first trip, the two children row over. The second trip, one child returns with the boat. The third trip, one adult rows to the other side. The fourth trip, one child returns with the boat. At this point, one adult has crossed the river. Repeat the first four trips an additional four times, one time for each adult. After completing the fifth time, there have been twenty trips taken, and the only people waiting to cross the river are the two children. On the twenty-first trip, the two children cross the river. So the minimum number of trips is twenty-one. Section 1.1 Objective A Exercises is units to the left of is 3 units to the right of < > < , 1, 16, 1, , 8, 7, 8, , 9, 77, 9, , 399, 66, 736, , 37, 377, 377, 37 Objective B Exercises 37. Five hundred eight 39. Six hundred thirty-five 1. Four thousand seven hundred ninety 3. Fifty-three thousand six hundred fourteen. Two hundred forty-six thousand fifty-three 7. Three million eight hundred forty-two thousand nine hundred five ,3 3., ,1, ,, , + 3, , , ,, Objective C Exercises > 718 rounded to the nearest ten is 711. is 7 units to the left of < < > > 96 rounded to the nearest hundred is.

2 Chapter 1: Whole Numbers ,1 = 8,1 rounded to the nearest hundred is 8, > 689 rounded to the nearest thousand is 7. 93,8 8> 93,8 rounded to the nearest thousand is 9,. 69,13 = 69,13 rounded to the nearest thousand is 63,. 3,876 < 3,876 rounded to the nearest ten-thousand is 3,. 71,83, 8> 71,83, rounded to the nearest million is 7,,. Objective D Exercises 89. Strategy To find the person with the greater number of stolen bases, compare the numbers 89 and < 937 Billy Hamilton had the greater number of stolen bases. 91. Strategy To find the greater number of performances, compare the numbers 8 and 3. 8 < 3 Fiddler on the Roof was performed the greater number of times. 93. Strategy To find the food which contains more calories, compare the numbers 19 and > 11 Two tablespoons of peanut butter contain more calories. 9. Strategy To find the shorter distance, compare the two numbers 189 and > 1833 The shorter distance is from St. Louis to San Diego. 97. Strategy To find the smaller planet, compare the two numbers 3, and 3,8. 3, > 3,8 Neptune is the smaller planet. 99. Strategy a. To determine the length of the State of the Union Address in 1, read the number in the bar graph above the 1 bar. b. To determine during which year the length of the State of the Union Address was longest, use the bar graph to find the year with the largest number above its corresponding bar. a. The length of the State of the Union Address in 1 was 67 minutes. b. The largest number appears above the bar corresponding to. The year in which the State of the Union Address was longest in. 11. Strategy To find the land area to the nearest tenthousand acres, round 161,6 to the nearest ten-thousand. 161,6 rounded to the nearest tenthousand is 16,. To the nearest ten-thousand acres, the land area of the Appalachian Trail is 16, acres. 13. Strategy a. To determine during which school year enrollment was lowest, use the line graph to find the school year corresponding to the lowest point on the line. b. To determine if enrollment increased or decreased between 197 and 198, read the graph at 197 and at 198. a. Student enrollment was lowest during the 198 school year. b. Enrollment was less in 198 than in 197. Enrollment decreased between 197 and Strategy To find the estimate of the speed of light, round the speed (99,8) to the nearest thousand. 99,8 rounded to the nearest thousand is 3,. To the nearest thousand, the speed of light is 3, km/s.

3 Section 1. 3 Applying the Concepts 17. The largest three-digit number is 999. (The next largest whole number is 1, which has four digits.) The smallest five-digit number is 1,. (The next smallest whole number is 9999, which has digits.) 19. a. True b. False, 87 rounded to the nearest hundred is 83. Section 1. Objective A Exercises 3. 73, ,6 1,383, ,8 + 66,37 11, , ,39, , 199,6 11,97 33, 3 97,16 6,8 78,31 37, ,13 + 8, 1 168, ,71 99, The total number of undergraduates enrolled at the college in 1 was , 1,. 97,8 1,, + 16,83 +, 1,388,917 1,, ,196, ,31 + 1, 39,81 37, 31. x + y x + y ,1 3. x + y 38,9 + 1, , 9 + 1,671 89, a + b + c

4 Chapter 1: Whole Numbers 39. a + b + c ,91 1. a + b + c 1, , ,897 36, ,1 3. The Commutative Property of Addition. The Associative Property of Addition 7. The Addition Property of Zero = ( + 17) = (9 + ) = = n = Yes, 38 is a solution of the equation h = No, 13 is not a solution of the equation = x = 3 Yes, 3 is a solution of the equation. Objective B Exercises // // / / / / / / / / 37 3,7 991 / / // / / // , / / /// 986, / / / / ,8 / / / / / , / / 3 / / / 67,87 17, / / 7 1 The difference between the maximum heights is 1 ft ,16 6,,83, 38, 83, , 87, 9 31,19 3,

5 Section ,196, 98,31 1, 1,66 1, 9. x y 37 1 / / x y / / x y / / / x y x y / /// x y 3, ,9 // // , = 3 y = 9 Yes, is a solution of the equation. 19. t 16= No, is not a solution of the equation z = 8 7 = Yes, 7 is a solution of the equation. Objective C Exercises 113. Strategy To find the sum of the whole numbers less than 1, add the numbers to = 1 The sum of the numbers is Strategy To find the difference, subtract 99 (the largest two-digit number) from 1 (the smallest four-digit number) The difference is Strategy To find the number of calories, add the number of calories in one apple (8), one cup of cornflakes (9), one tablespoon of sugar (), and one cup of milk (1) = 37 The breakfast contained 37 calories Strategy To find the perimeter of a rectangle, replace L with and W with 1 in the given formula and solve for P. P = L + W + L + W P = = 78 The perimeter is 78 m. 11. Strategy To find the perimeter of a triangle, replace a, b, and c with 16, 1, and 1 in the given formula and solve for P. P = a + b + c P = = 3 The perimeter is 3 in. 13. Strategy To determine the length of the hedge, by finding the perimeter of the playground, replace L with 16 and W with 1 in the given formula and solve for P. P = L + W + L + W P = = 6 The length of the hedge is 6 ft. 1. Strategy To find the difference in the number of orbits, subtract the number of orbits made by Apollo-Saturn 7 (163) from the number of flights made by Gemini- Titan 7 (6) Gemini-Titan 7 made 3 more orbits than Apollo-Saturn 7.

6 6 Chapter 1: Whole Numbers 17. Strategy To find the difference in seating capacity, subtract the seating capacity of Fenway Park (36,98) from the seating capacity of SAFECO Field (7,116). 7,116 36, 98 1,818 The difference in seating capacity is 1,818 seats. 19. Strategy To find the total cost of the computer system, add the cost of the operating system (83), the monitor (), the keyboard (17), and the printer (39) The total cost of the computer system is $ Strategy To find the estimate of the number of miles driven: Round the two readings of the odometer. Subtract the rounded reading from the beginning of the year from the rounded reading at the end of the year. 77,91 8, 8,376 6,, The car was driven approximately, mi during the year Strategy To determine between which two months car sales increased the most, find the difference, if there was an increase, between sales for January and February, February and March, and March and April for. Between January and February, : = Between February and March, : 1 13 = Between March and April, : not an increase Car sales increased the most between January and February of. The increase was cars. 13. Strategy To find the value of the investment, replace P by 1, and I by 77 in the given formula and solve for A. A = P + I A = 1, + 77 = 13,7 The value of the investment is $13, Strategy To find the mortgage loan, replace S by 9, and D by 9, in the given formula and solve for M. M = S D M = 9, 9, = 61, The mortgage loan on the home is $61, Strategy To find the ground speed, replace a by 37 and h by in the given formula and solve for g. g = a h g = 37 = 3 The ground speed of the airplane is 3 mph.

7 Section Strategy a. To determine how many drivers were traveling at 7 mph or less, add the numbers traveling 66 7 mph (3717), 61 6 mph (98), and less than 61 mph (87). b. To determine how many drivers were traveling at 76 mph or more, add the numbers traveling 76 8 mph (3) and more than 8 mph (178). a = drivers were traveling at 7 mph or less. b ,78 = drivers were traveling at 76 mph or more. 13. It is not possible to tell how many motorists were driving at less than 7 mph. The data shows that 3717 drivers were traveling at 66 7 mph. The number 3,717 includes motorists driving at 7 mph as well as those driving less than 7 mph (at speeds of mph). We cannot separate those driving at less than 7 mph from those driving at 7 mph. Applying the Concepts 1. If you roll two ordinary dice, the possible sums are the numbers (rolling two 1 s) through 1 (rolling two 6 s). Therefore there are 11 different sums possible. (The numbers are, 3,,, 6, 7, 8, 9, 1, 11, and 1). 17. a. Substituting any whole number for a in a = a will result in a true equation. The statement is always true. Section 1.3 b. Substituting any whole number for a in a a = will result in a true equation. The statement is always true. Objective A Exercises , , , , , , 6, = = = 1 =, = 1. q r s = qr s = qrs = 1,, = 1,, , 6, 9 3, 3 = 1,, 39,6 9 = 1,138, =, 7 63 = 6, = 6,3, = 6,91, ab 6 3 = 1, a 7 6 = 3

8 8 Chapter 1: Whole Numbers 3. xyz 13 = 63 = xy 67 3= 13 3 = The Multiplication Property of One 1. The Commutative Property of Multiplication = = 7. x = 6 ( ) = Yes, 6 is a solution of the equation x = = 3z 96 3( 3 ) No, 3 is not a solution of the equation 96 = 3z. 1. y = ( ) = 38 Yes, 19 is a solution of the equation y = 38. Objective B Exercises = = 3 c c= c 3 3 x x x y y y = x y = = = 1,, 3 6. ( ) ( ) = = 8 = ( ) ( 3 1 = = 9 1 = ( ) ( ) 6 = 6 6 = 36= = ( ) ( 3 3 3) 73. = 7 = 7 = 1 = 1 1 = 1 ) = = 6 8 = 1 a 3 x y 3 ( ) 3= 3 = 83 = 6 ab 6 ( ) = = 6 = 3 cd ( ) ( ) 3 = 3 3 = 9 = Objective C Exercises r , r

9 Section r r r , r r c d 36, 7, 7, = 8 36,7 7 = ,8, 76 8, 8 = 389,8 76 = 19 38,98, 79 8, 8 = 38,98 79 = 93 r37 33, 3, 19 3, = 1 33, 19 = 116 x y 8 1 = 8 x y 79 is undefined, because division by zero is undefined. x y 39, 98 39, z = 36 9 = Yes, 9 is a solution of the equation = x No, 9 is not a solution of the equation.

10 1 Chapter 1: Whole Numbers Objective D Exercises = 1 1 = 1 = The factors of 1 are 1,, and = 1 1 = = 1 = 3 The factors of 1 are 1, 3,, 6 and = 8 8 = 8 = The factors of 8 are 1,, and is prime number. The factors of 13 are 1 and = = = = 3 The factors of 18 are 1,, 3, 6, 9 and = = The factors of are 1, and = 6 6 = 8 6 = = = 7 The factors of 6 are 1,,, 7, 8, 1, 8 and = 8 8 = 1 = = The factors of 8 are 1,,, 7, 1 and = 8 8 = 8 3 = 16 8 = = = 6 The factors of 8 are 1,, 3,, 6, 8, 1, 16, and = = 7 3 = 18 6 = 9 9 = 6 The factors of are 1,, 3, 6, 9, 18, 7 and = = = 3 = = = = is a prime number = = 7 = = = = 3

11 Section Objective E Exercises 179. Strategy To find the estimate of the total cost: 167. Strategy To find the number of calories, multiply the number of calories in one ounce of cheese (11) by the number of ounces (). 11 = 6 Four ounces of cheese contain 6 calories Strategy To find the amount of jet fuel used, multiply the amount of fuel used each hour (86) by the time of flight (). 86 = 3 The flight used 3 gal of jet fuel Strategy a. To determine the perimeter of a rectangle, substitute for L and 1 for W in the formula below. b. To determine the area of a rectangle, substitute for L and 1 for W in the formula below. a. P = L + W P = + 1 = 78 The perimeter of the rectangle is 78 m. Round the number of suits to hundreds and the cost of each suit to tens. Multiply the rounded numbers = 16, The total cost of the suits is approximately $16, Strategy To find the total amount paid, replace M by 8 and N by in the given formula and solve for A. A = MN A = 8 = 68 The total amount paid on the loan is $ Strategy To find the time to drive the distance, replace d by 13 and r by 7 in the given formula and solve for t. b. A = LW A = 1 = 36 The area of the rectangle is 36 m Strategy To find the length of fencing needed to surround a square, substitute for s in the perimeter formula below. P = s = = 96 The length of fencing needed to surround a square is 96 ft. 17. Strategy To find the area of the two-car garage, substitute for s in the area formula below. A = s = = 76 The area of the two-car garage is 76 ft Strategy To find the amount of fabric needed for the flag, substitute 19 for L and 38 for W in the area formula below. A = LW = = 9,136 The amount of fabric needed for the flag is 9,136 cm. t = d r t = 13 = 9 7 It takes 9 h to drive 13 mi. 18. Strategy To find the value per share, replace C by 1,, and S by, in the given formula and solve for V. Applying the Concepts 1,, V = C = = 1 S, The stock has a value of $1 per share There are 7 days in one week. There are weeks in one year. 7 = 36 days. There are 36 days in weeks. There are 36 days in one year (366 days in a leap year). weeks in one year is an approximation.

12 1 Chapter 1: Whole Numbers 189. We need to find the smallest three-digit multiple of 6 that is a palindromic number. The smallest three digit palindromic number is 11; the next is 11; the next is 131. Any three-digit palindromic number that has a 1 in the hundreds place must have a 1 in the ones place. No number that has a 1 in the one s place is divisible by 6. The smallest three-digit palindromic number with a in the hundreds place is, which is not divisible by 6. The next smallest is 1, which is not divisible by 6. is the smallest three-digit multiple of 6 that is a palindromic number (7) = = (8 3) 1 = 6() 1 = 3 1 = (13 ) = 16 8 = 16 = = = = 18 = x y 8 3 = 8 6 = Section Objective A Exercises = + =. 6 + = + = = 16 3= (6 3) + = 3 + = 1 + = (7+ ) 6= = 9+ = (1 + ) 13 = = = = + 7 = = = 1 + = (8 ) 3 = = = = + = 8+ = = 1. ( ) 3. ( ) ( ) = = = + 1 = x + 3y = = = 7 x y x = + 8 = + = x + ( x y) ( ) = = = = 68 = 1. 3( ) x + x y + z ( ) = = = = 7+ 9 = (8 + ) 6 = = 11+ = (9 ) 3 = = = Since > 13, 1 + (9 ) 3 > 11 + (8 + ) 6

13 Chapter Review Exercises 13 Applying the Concepts = = = 81 6 = 17 (1 ) = (8) = = = + 36= 6(8) = 8 = (1 + ) 1 = () 1 = () 1 = 1 = Since > 17 > 11 > 1 > >, > 81 8 > > (1 ) > (1 + ) 1 > 6(8) Chapter Review Exercises = 1, = ,79 < 38,79 rounded to the nearest hundred is 38, > ,9 9. xy 7 = 1 7 = , = = = 1 1 = The factors of are 1,,, 1, and. 1. y = = 17 Yes, 7 is a solution of the equation = = = = 16 + = ( ) 16. The Commutative Property of Addition 17. Four million nine hundred twenty-seven thousand thirty-six x y 3 ( ) ( 3 = 333 = 7 = 67 ) 19. Strategy a. To determine by many times more PG-13 films were released than NC-17 films: Find the number of PG-13 films (11) and the number of NC-17 films (7) from the pie chart. Divide the number of PG-13 films by the number of NC-17 films. b. To determine by many times more R rated films were released than NC-17 films: Find the number of R rated films (7) and the number of NC-17 films (7) from the pie chart. Divide the number of R rated films by the number of NC-17 films. a = There were 16 times more PG-13 films released than NC-17 films. b = There were 61 times more R rated films released than NC-17 films.

14 1 Chapter 1: Whole Numbers r Strategy To find the total cost, multiply the number of square feet of floor space (8) by the cost per square feet (6). 8 6 = 18, The total cost of the contractor s work will be $18,. 3. Strategy a. To find the perimeter of the rectangle, substitute for L and 1 for W in the formula below.. x y = 137 b. To find the area of the rectangle, substitute for L and 1 for W in the formula below = 3 3 = 3 x y =. 1 8 = = = 8 8 = 1 7. x + y = (a + b) c ( ) + 3 = 8 = 6 = 6 8 = 6 a. P = L + W P = + 1 P = + P = 7 The perimeter is 7 m. b. A = LW A = 1 =3 The area is 3 m. 33. Strategy To determine between which decade the number of students enrolled in college increased the most, and the amount of increase, find the amount of increase for each decade. Then compare the numbers. 196 to 197: 8,81, 3,789, =,79, 197 to 198: 1,97, 8,81, = 3,16, 198 to 199: 13,819, 1,97, = 1,7, 199 to : 1,889, 13,819, = 1,7,,79, > 3,16, > 1,7, > 1,7, a. The number of students enrolled in college increased the most from 196 to 197. b. The amount of increase was,79, students. 3. Strategy To find the person with the greater number of rebounds, compare the numbers 17, and 16, Strategy To find the distance traveled, substitute 3 for t and 1 for r in the given formula and solve for d. 17, > 16,79 Kareem Abdul-Jabbar had more rebounds. d = rt d = 1 3 = The cyclist traveled mi.

15 Chapter Test 1 3. Strategy To find the markup, substitute for S and 177 for C in the given formula and solve for M. Chapter Test = 39,7 M = S C M = 177 = 9 The markup on the copy machine is $ = 16, x x x x y y y = x y 3. 3 = p = p = p Yes, 7 is a solution of the equation > 961 rounded to the nearest hundred is < Three hundred eighty-two thousand nine hundred four , ,79, 6, 6 =,, = 9 9 = 6 9 = = The factors of 9 are 1,,, 3, 6 and = 3 = 3 1. x y 39,1 837 = 3, The Commutative Property of Addition 17. x y 388 = (1 3) 9 = = 7 1 = ,3 3, = $13, ( 3) = + (1) = + (1) = + = x + (x y) 8 + (8 ) = + = + 16 = 6 The solution is (3 + 7 ) x = 3 + (7 + x) = 7. Strategy First, to find the total cost of the computer system, add the prices of the components. Then, to find the balance of the checking account, subtract the total cost of the computer system from $ = = 6 The balance is $6.

16 16 Chapter 1: Whole Numbers 6. Strategy a. To find the perimeter of the square, substitute for s in the formula below. b. To find the area of the square, substitute for s in the formula below. a. P = s P = =96 The perimeter is 96 cm. b. A = s A = () =76 The area is 76 cm. 7. Strategy To find the data processor s take home pay, subtract the sum of his deductions, taxes (8), retirement (7), and insurance (18), from the total salary (69). 9. Strategy To find the commission earned, substitute for U and 8 for R in the given formula and solve for C. C = U R C = 8 = 96 The commission earned is $ Strategy To find the value per share of the fund, substitute,, for C and, for S in the given formula and solve for V.,, V = C = = 11 S, The value per share is $ ( ) = = 6 The data processor s take home pay is $6. 8. Strategy a. To determine between which two years the number of vehicles sold increased the most, for year there was an increase, find the increase. Then compare the numbers. b. The amount of increase is the largest amount to 1999,, = 3, 1999 to 13,, = 8, to 1 17, 13, =, 1 to 3, 17, = 1, 1, > 8, >, > 3, a. The number of vehicles sold increased the most from 1 to. b. The amount of increase was 1, vehicles.